Stefan problems and the Penrose-Fife phase field model

This paper is concerned with singular Stefan problems in which the heat flux is proportional to the gradient of the inverse absolute temperature. Both the standard interphase equilibrium conditions and phase relaxations are considered. These problems turn out to be the natural limiting cases of a thermodynamically consistent model for diffusive phase transitions proposed by Penrose and Fife. By supplying the systems of equations with suitable initial and boundary conditions, a rigorous asymptotic analysis is performed, and the unique solutions to the different Stefan problems are derived as asymptotic limits of the solutions to the Penrose-Fife phase-field problem